Firms A and B are in a market of fixed size (Size = 1), developing a product for their customers. The more R and D they undertake i.e. the more time they spend, the better product they are able to launch in the market. However, the firms are facing a constraint; whoever launches their product first, will gain a market share of customers that cannot be transferred to their opponent. In this case the opponent will obtain the remainder of the customers in the market. If both A and B launch their product at the same time, the share of customers will be equally divided amongst them.

Each firm has to choose time t at which they will launch their product in the market. The share of customers in the market is defined by the function f(t)=twhere f(0)=0 and f(1)=1 (The share of customers in the market is a function that increases over time with the lowest share being 0 and the maximum share of customers equal to 1). Assume time and hence market share of customers is perfectly divisible over the spectrum of time defined as t = {0..............1}. Hint: This means that any fractional amount of time and hence market share is possible 1/3,1/4, 1/6 etc etc